Question

A truck with wheels of radius 01.4 m moves without slipping on a muddy track. A dirt particle files off from the top of the wheel and lands on the ground at a horizontal distance (distance from the base of the wheel) of 6 meters from the point where the dirt particles files off the wheel. Find the speed of the truck. Also find the distance between the wheel's base and the point where the dirt particle lands at the time instant the particle hit this ground.

• A. 7.5 m/s, 3 m
• B. 6.5 m/s, 3 m
• C. 7.5 m/s, 5 m
• D. 6.5 m/s, 2 m

Answer 1

The correct option is A 7.5 m/s, 3 m

At point $A,we=v$

At point $B$

$VB=v+WR=2V$

For pure rolling,

$VB=2V,$ where $V$ is the velocity of $COM$

So, the initial velocity of clit $=VB$

$=2V$

Let $t$ is the time of height

Then,

By $2^{nd}e{q}^n$ of motion,

$-2R=\left(o\right)t-g_2{t}^2$

$\sqrt{\frac{4R}{g}}=t$

$st=\sqrt{\frac{4\left(0.4\right)}{10}}=0.43$

Also,

$\left(2v\right)\left(t\right)=3$

As, $s=6m$

$\Rightarrow v=\frac{3}{2t}=\frac{6}{2\left(0.4\right)}=7.5m/s$

Distance travelled by the base

$d=v\left(t\right)=7.5\times 0.4$

$d=3m$

Distance b/w the dirt and base

$=3-d=6-3=3m$

Option $A$ is correct.